Date of Award

Fall 2011

Document Type


Degree Name

Doctor of Philosophy (PhD)


Biomedical Engineering

First Advisor

Silver-Thorn, M. Barbara

Second Advisor

Heinrich, Stephen M.

Third Advisor

Toth, Jeffrey M.


Commercially available orthopaedic implants have a bending stiffness (flexural rigidity) that is at least 10 times greater than cortical bone. Effects of this stiffness mismatch have been extensively studied relative to total hip arthroplasty (THA). Clinical experience with THA has shown that stiffness mismatch is the primary cause of accelerated bone resorption due to the stress shielding, resulting in sub-optimal bone loading, aseptic loosening and inadequate bone support for a future revision implant.

Attempts to incorporate design features that reduce the flexural rigidity of implants have yielded inconsistent results or failures due to biomaterial incompatibilities and practical manufacturing complications. The recent development of additive manufacturing (AM) processes allow the fabrication of closed-cell porous Ti or CoCr microstructures as a practical means of fabrication while reducing implant stiffness.

The use of engineered porosity to modify flexural rigidity requires an ability to predict moduli from microstructural parameters. The literature is replete with different formulas which are often contradictory; existing equations relating porosity to effective moduli are generally interpretive and not predictive.

This study applied finite element methods to three-dimensional porous structures with different arrangements of spheroidal voids. The resulting data show that the effective Young's modulus varies linearly with &psi, the ratio of pore radius to center-to-center dimension, for a porosity range of 20 to 50%. In addition, the arrangement of spherical voids was found to have only a minimal effect on the resultant Young's modulus. Predictive equations for Poisson's ratio are second-order and dependent upon the void arrangement. The effect of changes in loading direction on moduli indicate that the three microstructures evaluated in this study are anisotropic, with anisotropy increasing with both ψ and volume porosity. The predictive equations developed in this study were validated with AM fabrication and testing of prototypical Ti6Al4V spinal rods. Constructs of a rhombohedral (FCC) pore arrangement with 30% porosity showed an effective reduction of ~ 50% in Young's modulus. Predicted values for flexural rigidity fell within 95% confidence intervals for the tested porous Ti6Al4V constructs, confirming a design methodology with the potential of reducing the flexural rigidity, and resulting bone resorption, of orthopaedic implants.